Section 11 EO C440.09 – DESCRIBE THE RELATIONSHIP BETWEEN GRAVITY AND SPACE-TIME

According to Newton’s theory of gravity, all bodies possess the force of attraction called gravity. Larger masses, such as the Sun, attract smaller masses, such as the planets and comets, more strongly, causing the smaller masses to move toward the larger masses. In our solar system, the planets orbit the Sun due to the force of the Sun’s gravity pulling them into this elliptical path. Comets soaring through the galaxy are curved toward the Sun due to gravity’s pull.

In Principia (1687), Newton stated, “there is a power of gravity pertaining to all bodies, proportional to the several quantities of matter which they contain.” However, when Newton was questioned about how this “power of gravity” transmitted from one body to another, he responded, “I make no hypothesis.”

Einstein, along with other scientists, began to question this conclusion around the turn of the 20^th century. In the 19^th century, Maxwell had shown that light propagated at a finite rate in a vacuum; 299 792 km / sec (185 871 miles / sec). In 1905, Einstein’s theory of special relativity was based on the idea that this rate was the speed limit for all matter and energy in the universe. If gravity was a force that transmitted between masses in the same way light propagated through space, the force of gravity should be equally restricted to 299 792 km / sec. While moving nearly 300 000 km each second is extremely fast, it is not instantaneous.

Newton believed that space and time were absolute or fixed entities and that gravity could be represented as an attractive force that somehow acted instantaneously between objects. Einstein determined that space and time are relative entities, interwoven into a “fabric,” which he called space-time, and he realized that no force—not even gravity—could act faster than the speed of light. In Einstein's universe, the presence of celestial bodies causes space-time to warp or curve; and gravity is not a force, but rather the product of bodies moving in curved space-time.

Since space and time were separate concepts in Newton’s physics, an object's position is simply described by three spatial coordinates. In Einstein’s physics, space and time are combined into space-time so that when describing the position of an object one must include all four dimensions—the three spatial dimensions and time. The passage of time is relative to motion, so the time coordinate in the description of position describes time relative to a frame of reference, which is absolutely critical in Einstein’s relativity.

Show the cadets the WMV video file Einsteins_Universe_Anima. Running time is 1 minute, 9 seconds.

In 1916, Einstein presented the world with this new understanding of the universe—his general theory of relativity. In his theory, space is not an empty void, but an invisible structure called space-time. Nor is space simply a three-dimensional grid through which matter and light and energy move. It is a four-dimensional structure called space-time whose shape is curved and twisted by the presence and motion of matter and energy.

Space-time curves around any mass. The presence of planets, stars and galaxies warps the fabric of space-time in a manner similar to a bowling ball warping a spandex sheet. The mass of the ball stretches the fabric and creates a dip or curve that gradually decreases the further one moves from the mass.

When a mass passes near a larger mass, it accelerates toward the larger mass because space-time itself is curved toward the larger mass. The smaller mass is not “attracted” to the larger mass by any force. The smaller mass simply follows the structure of curved space-time near the larger mass. For example, the massive Sun curves space-time around it, a curvature that reaches out to the edges of the solar system and beyond. The planets orbiting the Sun are following the curvature of space-time by the Sun.

Show the cadets the WMV file Rel_gyro_expt-anima. Running time is 3 minutes, 1 second.

The gyroscope is a spinning wheel (rotor) in a universal mounting (gimbal) that allows its axle to be pointed in any direction.

Also known as rigidity in space, gyroscopic inertia is the tendency of a rotating object to remain in its plane of rotation. This allows the spin axis of a gyroscope to remain unchanged regardless of how the gimbal is moved around it.

Show the cadets the slide of Figure A-1 located at Attachment A.

Examples of rotating objects that exhibit rigidity in space are tops, gyroscopes, Frisbees, basketballs and any spinning planet. These objects tend to maintain their orientation in space.

Aircraft use gyroscopes for navigation, with the gyroscope maintaining the orientation of the universe so that relative changes in the aircraft's orientation can be measured. In the Gravity Probe B (GP-B) satellite, the gyroscope maintains its orientation relative to a distant guide star so that the changes in the orientation of space-time near Earth can be measured.

To work properly, the rotor must be kept spinning at a constant speed. Gyroscopic instruments may be powered by one or more power sources. In an aircraft, a gyroscope can be powered by moving air systems. In the GP-B satellite, the gyroscopes are powered by helium gas that is stored as liquid in the largest satellite component: the dewar.

Dewar. A double-walled vessel with a vacuum between the walls to reduce the transfer of heat, used for storing hot or cold liquid.

Show the cadets the slide of Figure A-2 located at Attachment A.

Spin a coin on its edge to show the cadets that it will remain upright while spinning. Demonstrate that the coin will not remain upright on its edge when it is not spinning.

It was predicted that the spin axis of each of GP-B's four gyroscopes move with the curvature and twist of local space-time around Earth. The only way this motion can be detected is by comparing each spin axis to a fixed line of reference. In this mission, the fixed reference line is the line between the telescope and the guide star: IM Pegasi. The telescope has to remain fixed on the exact centre of the guide star (within one milliarcsecond, or 1 millionth of an inch) throughout the mission or GP-B would lose its single critical reference line.

SQUID (Superconducting QUantum Interference Device). A device that monitors the spin axis orientation of the supercooled, superconducting gyroscope's perfectly unmarked, spherical rotor—without exerting significant torque on the spinning rotor.

Show the cadets the WMV video file SConSquid. Running time is 2 minutes, 12 seconds.

Einstein’s theory predicted that the presence of a mass in space, such as the Earth, will warp local space-time, creating a dip or curve in space-time. This is called geodetic effect.

One of the predictions of Einstein’s general theory of relativity is that local space-time is twisted by the rotation of the Earth—any rotating mass will drag the local space-time frame of reference with it. The predicted drag is very small and fades as one travels further from the rotating mass, but the twist nearby can affect the paths of light, energy, and other masses.

Show the cadets the WMV video file Simple_expt_anima. Running time is 1 minute, 7 seconds.

The GP-B satellite is composed of thousands of components, but the mission can be understood by considering only a few, to include:

Show the cadets the WMV video file DF-Satellite. Running time is 4 minutes 25 seconds.

Astrophysicists at York University measured and tracked the movement of GP-B's guide star, IM Pegasi, against a backdrop of more distant quasars. This allowed minute changes in the position of IM Pegasi to be taken into account when changes in gyroscope orientation was measured—in a system where angles of a millionth of a degree are of critical importance.

Quasar. Any of a class of starlike celestial objects, apparently of great size and remoteness, often associated with a spectrum with a large red shift and intense radio emission.